In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is approximately 0.542 multiplied by 10-10 m. (The actual value is 0.529 multiplied by 10-10 m.)

Question

In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is approximately 0.542 multiplied by 10-10 m. (The actual value is 0.529 multiplied by 10-10 m.)
(a) Find the electric force exerted on each particle, based on the approximate (not actual) radius given. 
  N

(b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron? 
  m/s

Elena · Answer

F=k•q₁•q₂/r²
k =9•10⁹ N•m²/C²
e =1.6•10⁻¹⁹ C.

F=k•e²/r²=
=9•10⁹•(1.6•10⁻¹⁹)²/(0.542•10⁻¹⁰)² =
=7.84•10⁻⁸ N
ma=mv²/R= F
v=sqrt(FR/m)=
=sqrt(7.84•10⁻⁸•0.542•10⁻¹⁰/9.1•10⁻³¹)=
=2.16•10⁶ m/s